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Deformation-induced coupling of the generalized external actions in third-gradient materials. (English) Zbl 1500.74008

Summary: In this study, diverse typologies of external actions are outlined, which turn out to be admissible for the third-gradient modeling of elastic materials. It is shown how such loading, when prescribed over the boundary surface, along the border edges and at the wedges of a deformable body in the Eulerian configuration, can be transformed into the Lagrangian description generating multiple interactions, with a surprising deformation-induced coupling. Such a phenomenon becomes more and more important at increasing the order of the \(\beta\)-forces, specified by duality as covectors expending work on the \(\beta\)th normal derivative of the virtual displacements, being herein at most \(\beta =2\). Insights are provided into the true nature of such generalized forces, resting on the differential geometric features of the deformation process.

MSC:

74B20 Nonlinear elasticity
74A20 Theory of constitutive functions in solid mechanics
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